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## Measuring Risk

The main problem with risk calculations is that it requires us to predict the future.

• During stable periods, the past may be a good predictor of the future, so we can use historical data.

• In periods of crisis, however, the future may behave differently from the past rendering historical data irrelevant.

• It is precisely in the latter type of period that we need good measures of risk. In other words, risk measures tend to work well until you need them.

For an introduction to risk in financial markets see A First Look at Risk.

## Review of Return Description

To implement any measure of risk we must have a description of how the asset’s returns behave.

• This is described by a probability density function (PDF).

• For all intervals, the PDF assigns a probability that an asset’s return will be within each interval in a given period. For example, the PDF may say there is a 7% probability the asset’s return will be between 1% and 2% over the next day.

## Let’s Take a Look

In the following app you can see how stock returns distributions behaved over different time periods.

• Generally, the lower the peak of the distribution, the higher the risk (possible returns are spread over a wider interval of returns).

• Be sure to move the 3D graphic around and zoom in and out to get a better look.

• Try and compare small stocks with the distributions on portfolios of large numbers of stocks. For example, take a look at EGAS and then SPY. EGAS is a small Natural Gas distributor and SPY is an ETF which tracks the S&P 500. Are there differences between how risk varies between the two?

• The app may take 5 seconds or so to load.

## Predicting Risk: Models

We do have various methods to predict risk, such as the ARCH/GARCH class of models and predictions from Kalman Filtering and Markov Switching algorithms. In these models, however, future risk is a function of past risk, and so in low-risk periods the models will predict low risk in the future, and for high-risk periods, they will predict high risk in the future. This makes sense, because we know volatility clusters.

• What these models won’t tell us is when we’ll transition from low to high risk periods. This transition point is a very valuable piece of information.

## Predicting Risk: Expectations

Given the weakness of the econometric method of predicting risk, most focus on market-based estimates. Expected risk is an important component of option prices. So we can observe option prices to get an idea of what market participants expect risk to be in the future.

• This method works well when there are known eventssuch as an option earnings season. However, it will fail if the events are unforeseen, such as the BP Gulf of Mexico oil spill.

• A commonly cited measure of overall market risk is the VIX. There is even an expected volatility of this VIX in the VVIX.

## Credits and Collaboration

Click the following links to see the codeline-by-line contributions to this presentation, and all the collaborators who have contributed to 5-Minute Finance via GitHub.